Simplify the following expression and state the condition under which the simplification is valid. $q = \dfrac{y^2 - 25}{y - 5}$
Answer: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = y$ $ b = \sqrt{25} = -5$ So we can rewrite the expression as: $q = \dfrac{({y} {-5})({y} + {5})} {y - 5} $ We can divide the numerator and denominator by $(y - 5)$ on condition that $y \neq 5$ Therefore $q = y + 5; y \neq 5$